unable to isolate the product of the reaction between
pyrrolidine and 2, monitoring by NMR showed quantita-
tive conversion to a species identified as the Et-triazane, by
6
comparison to spectra of the isolated iPr-triazane. Pre-
vious work has shown that while iPr and tBu triazanes
are isolable, the Et and Bn forms are prone to decompos-
7
c,d
ition.
The relative reactivities of the azodicarboxylates
toward amines do, however, appear to follow their relative
9
reactivity toward enamines and phosphines.
These off-cycle processes may help to rationalize the
three distinct rate regimes observed in this reaction. The
intrinsic reaction kinetics of the cycle are manifested in the
high initial rate. The formation of 5 is implicated in the
rapid decrease in this initial rate, which occurs as a large
fraction of the active catalyst is rapidly siphoned away
from the productive catalytic cycle. The stability of 5
rationalizes the anomalous negative reaction order in [2]
shown in Figure 2, because the concentration of 4b within
the catalytic cycle decreases with increasing [2]. The rate
acceleration observed at the end of the reaction, where
conditions of low [2] and high [1] prevail, occurs as a larger
fraction of 4b is released from the off-cycle reservoir and
becomes available to the cycle. Similar anomalous kinetics
have been observed in Pd-catalyzed amination reactions
Figure 3. Comparison of experimental (open circles) and simu-
lated (solid lines) reaction rate profiles as a function of time for
the mechanism of eqs 2ꢀ4 using 0.035 M catalyst 4b and initial
concentrations [1] = 1.5 M and (a) [2] = 0.4 M; (b) [2] = 0.7 M;
and (c) [2] = 0.8 M. Best fit of eqs 2ꢀ4 to the data obtained with
ꢀ
1
ꢀ1
K
ꢀeq = 42 M and kr.d.s. = 0.5 M /min; rate constant for the
(
arbitrarily high value (10
kinetically not meaningful) product formation step set at an
1
2
ꢀ2
M /min). Kinetic modeling carried
out using Copasi (COmplex PAthway SImulator) v. 4.5.
9
4
b
due to an off-cycle reservoir.
Kinetic simulations reveal that all of the features of the
unusual kinetic profiles shown in Figure 1 may be accu-
rately reproduced with the simple set of elementary steps
given in eqs 2ꢀ4, containing the equilibrium constant, K ,
eq
for reversible formation of 5, and the rate constant for
enamine formation, kr.d.s., as the only adjustable para-
meters (Figure 3). The simulation demonstrates the build-
up of 5 early in the reaction, predicting that as much as
8
0% of the catalyst 4b is siphoned off the cycle in the form
of species 5 under conditions of high [2] (Figure 4).
Throughout the course of the reaction, 5 remains the
dominant intermediate.
Figure 4. Partitioning of catalytic species over the course of the
reaction predicted from the simulation of the reaction under the
conditions shown in Figure 3c.
Keq
2
þ 4b
a
5
ð2Þ
Understanding the role of the off-cycle reservoir leads to
suggestions for optimizing the reaction’s productivity by
seeking ways to minimize the buildup of species 5. One
approach aims to retain the catalyst within the cycle by
maintaining high concentrations of 1 and low concentra-
tions of 2, thereby decreasing the driving force for forma-
tion of 5 and preventing its accumulation by allowing more
effective competition from the desired amination reaction.
An experimental protocol was devised with a slow addition
of 2 over time to a vial containing aldehyde 1 and catalyst
4b. Figure 5 shows that under optimized “semibatch”
operation, the rate of addition of 2 is roughly equal to its
rate of conversion to product for more than 50% conver-
sion, which prevents a buildup of 2, and therefore of 5, in
the system. The reaction is complete within 25 min, or a
factor of 8 times faster than the standard protocol mixing
all reactants simultaneously. A turnover frequency of 1.25
Kr:d:s:
s
1
þ 4b
f
enamine þ H2O
ð3Þ
ð4Þ
enamine þ 2 þ H2O f 3 þ 4b
The simulations confirm previous findings that the rate-
determining step within the cycle is formation of the
0
enamine. The intrinsic reaction is first-order in [1], which
1
participates in the rate-determining step, and zero-order in
[
2], which enters the cycle after the rate-determining step.
Thus the deceptively complex experimental rate profiles
are revealed to arise from the simple one-step intrinsic
kinetics of the catalytic cycle coupled with an off-cycle
reservoir equilibrium.
(
9) Hoops, S.; Sahle, S.; Gauges, R.; Lee, C.; Pahle, J.; Simus, N.;
Singhal, M.; Xu, L.; Mendes, P.; Kummer, U. Bioinformatics 2006, 22,
067.
10) (a) Mathew, S. P.; Klussmann, M.; Iwamura, H.; Wells, D. H.,
Jr.; Armstrong, A.; Blackmond, D. G. Chem. Commun. 2006, 4291. (b)
Zotova, N.; Moran, A.; Armstrong, A.; Blackmond, D. G. Adv. Synth.
Catal. 2009, 351, 276.
ꢀ
1
min is achieved under these conditions.
3
(
A second approach for improved productivity focuses
on increasing the free catalyst concentration by catalyzing
the decomposition of 5 back to 2 and 4b. The effect of acid
4
302
Org. Lett., Vol. 13, No. 16, 2011